写一个Matlab从配送中心出发,连接其它点,并使路线长度之和最短
时间: 2024-03-02 08:49:10 浏览: 79
matlab.zip_matlab路网_workerfgo_多点最短路径_多点路径
您的问题涉及到的是一个典型的旅行商问题(Traveling Salesman Problem,TSP),是一个NP难问题,通常使用启发式算法求解。以下是一个使用遗传算法(Genetic Algorithm,GA)求解TSP的Matlab代码示例:
```matlab
% 配置参数
popSize = 50; % 种群大小
numCities = 20; % 城市数
maxGen = 500; % 进化代数
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
% 生成随机城市坐标
cities = rand(numCities, 2) * 100;
% 初始化种群
pop = zeros(numCities, popSize);
for i = 1:popSize
pop(:, i) = randperm(numCities);
end
% 进化过程
for gen = 1:maxGen
% 计算适应度值
dist = zeros(popSize, 1);
for i = 1:popSize
dist(i) = sum(sqrt(sum((cities(pop(:, i), :) - circshift(cities(pop(:, i), :), [1, 0])).^2, 2)));
end
fitness = 1./dist;
fitness = fitness./sum(fitness);
% 种群选择
[val, idx] = sort(fitness, 'descend');
elite = pop(:, idx(1));
pop = pop(:, idx(1:popSize-1));
prob = cumsum(val);
prob = prob/prob(end);
for i = 1:popSize-1
a = find(rand() <= prob, 1);
b = find(rand() <= prob, 1);
if rand() <= pc
% 交叉
c = randi(numCities-1);
d = randi([c+1, numCities]);
child = [pop(1:c, a); pop(c+1:d, b); pop(d+1:end, a)];
child = unique(child);
if length(child) < numCities
% 补全缺失的城市
missing = setdiff(1:numCities, child);
child = [child; missing];
end
pop(:, i) = child;
else
% 复制
pop(:, i) = pop(:, a);
end
end
% 变异
for i = 2:popSize-1
if rand() <= pm
a = randi(numCities);
b = randi(numCities);
pop([a, b], i) = pop([b, a], i);
end
end
% 加入精英
pop(:, end) = elite;
end
% 输出最优解
dist = zeros(popSize, 1);
for i = 1:popSize
dist(i) = sum(sqrt(sum((cities(pop(:, i), :) - circshift(cities(pop(:, i), :), [1, 0])).^2, 2)));
end
[val, idx] = min(dist);
fprintf('最短路程长度:%f\n', val);
fprintf('最短路程路径:');
fprintf('%d -> ', pop(:, idx));
fprintf('%d\n', pop(1, idx));
```
该代码使用遗传算法求解TSP问题,将城市坐标随机生成,通过进化过程逐步优化种群中的路线。最终输出最短路程长度和路径。您可以根据实际情况进行参数调整和优化。
阅读全文